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Electron paramagnetic resonance in Y1−cH1.92:Erc
~
S o l i d S t a t e Coaununications, V o i . 3 6 , p p . 9 8 9 - 9 9 3 . Pergamon P r e s s L t d . 1980. P r i n t e d i n G r e a t B r i t a i n .
ELECTRON PARAMAGNETIC
RESONANCE
C. M. J a c k s o n , J . E l l l o t t , Department
of Physics,
IN Yl_cHi.92:Erc
M. Hardlman, R. Orbach
University of California,
Los Angeles,
CA 90024
and G. K. Shenoy Argonne National Laboratory, Argonne, llllnois 604]5 (Received 25 August 1980 by A. A. Maradudin)
We have investigated t h e EPR of Isotoplcally enriched ISSEr 3+ in YI_cHI.92:Er c where c = i00 and 1400 ppm, at both 1.4 and 9 GHz and between 1.5 and 50 K. Resonance lines were observed from Er 3+ ions in both sites of cublc.symmetry and sites of axial symmetry. We determine the 3~ numbers of Er in cubic, and C. axial symmetry to be in the ratio 2:1. The cubic site resonance llne ~v is at g = 6.85 ± 0.07 and is attributed to a r7 doublet. The llnewtdch has a linear thermal broadening of 3,9 ± 0.05 gauss K -l below circa 7 K. From the nonlinear thermal broadening above this temperature we determine the first excited state, in the cubic crystal field scheme, to be a F8 at 35 ± I0 K above the r7 ground state. We have investigated the origins of the (T - O) residual linewldth for the ions in cubic symmetry, and conclude there to be a small but significant contribution due to unresolved transferred hyperflne structure from the surrounding hydrogen n u c l e i .
The m e t a l d l h y d r l d e s YH:, ErH~, and ScHz a l l have t h e f l u o r i t e (CaF2) s t r u c t u r e . This consists of a simple cubic array of protons with m e t a l i o n s o c c u p y i n g e v e r y o t h e r cube c e n t e r . The m e t a l i o n t h u s o c c u p i e s a s i t e o f c u b i c symm e t r y w i t h c o o r d i n a t i o n number (CN)8. M~ssbauer s t u d i e s 1'2 o f Er ~ doped YH2 have i d e n t i f i e d this cubic site. However, e l e c t r o n paramagneclc r e s o n a n c e (EPR) s t u d i e s s on Er sT doped ScH2 i n d i c a t e t h a t , in s~dicion to the expected cubic symmetry, t h e Er 3 i o n o c c u p i e s a t l e a s t one and p o s s i b l y two t y p e s o f s i t e s w i t h a x i a l synunetry. We r e p o r t h e r e . t h e r e s u l t s o f our EPR meas u r e m e n t s on 16SErS~ i n YHI.92:Er. These meas u r e m e n t s were c a r r i e d o u t wlch s e v e r a l o b j e c t i v e s i n v i e w . We wished ( i ) to d e t e r m i n e t h e p r o p o r t i o n o f a x i a l s i t e s , t h e p r e s e n c e o f which had b e e n r e p o r t e d e a r l i e r , ~ ( l i ) t o i n d e p e n d e n t l y confirm the f e a t u r e s of the c r y s t a l e l e c t r i c f i e l d (CEF) a t t h e c u b i c s i t e s a s d e t e r m i n e d l p r e v i o u s l y , and ( i l l ) t o i n v e s t i g a t e t h e o r i g i n s o f t h e (T " 0) r e s i d u a l EPR l l n e w l d t h , i n p a r t l c u l a r the p o s s i b i l i t y of unresolved t r a n s f e r r e d h y p e r f i n e s t r u c t u r e i n t h e Er m+ r e s o n a n c e due t o t h e s u r r o u n d i n g h y d r o g e n n u c l e l . + The c o n v e n t i o n a l llamiltonlan f o r Er 3 , J 1512, i n a c u b i c c r y s t a l f i e l d i s , a f t e r Lea, L e a s k , and Wolf, s
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These e n e r g y l e v e l s a s f u n c t i o n s o f X and W a r e shown i n F i g . 1. The M ~ s s b a u e r ~ t u d i e s | ' 6 o f ¥H2:Er i n d i c a t e t h a t t h o s e Er J" i o n s i n s i t e s w l t h c u b i c symmetry e x h i b i t a s m a l l low t e m p e r a t u r e Korrlnga relaxation rate. P r e v i o u s works on o t h e r s y s t e m s 7 ' s have t a k e n a d v a n t a g e of s m a l l t h e r m a l b r o a d e n i n g t o examine t h e a d d l t l o n a l b r o a d e n i n g o f t h e EPR l i n e w l d t h produced by t h e r m a l p o p u l a t i o n o f c r y s t a l f i e l d s t a t e s above t h e ground state. This i n t u r n a l l o w s a d e t e r m i n a t i o n o f t h e e n e r g y s e p a r a t i o n between t h e ground and first excited states. We have a p p l i e d t h i s a p p r o a c h t o our m e a s u r e m e n t s . Two samples of Yl_cHi.92:Erc , wlth c = I00 and 1400 ppm, were prepared by doping YHI 92 with Isotropically enriched freEr in a manner described elsewhere. I The 16SEr was 95% abundant, the laVEr 3% abundant, and the r e s i d u e made up of other Er isotopes. The low concentration of 167Er was verified by the low intensity of the 16VEt hyperflne lines in the EPR
spectra. The powdered s a m p l e s were found to c y c l e r e p e a t e d l y t o low t e m p e r a t u r e w i t h o u t any change in t h e s p e c t r a . A l l EPR measurements were made u s i n g homodyne s p e c t r o m e t e r s o p e r a t i n g a t 1.4 and 9 GHz and o v e r t h e t e m p e r a t u r e r a n g e 1.2 t o I00 K. The low f r e q u e n c y measurements were s i g n a l a v e r a g e d when n e c e s s a r y . Temperat u r e s were d e t e r m i n e d by v a p o r p r e s s u r e t h e r m o merry below 4.2 K and by t h e r m o c o u p l e s a t h i g h e r temperatures. F i g u r e 2 shows a t y p i c a l low t e m p e r a t u r e EPR s p e c t r u m , which a t b o t h f r e q u e n c i e s d i s p l a y s an i n t e n s e l l n e b e t w e e n a p a i r of weaker " ~ a t e l 1 ire " lines. The intense llne is from Er 3 ions i n c u b i c symmetry; the o b s e r v e d g - v a l u e of 6.85 ± 0.07 i s v e r y c l o s e t o t h e g = 6.8 e x p e c t e d
(~)
w h e t s O~ and O~ a r e t h e S t e p h e n s O p e r a t o r s , W i s t h e o v e r a l l m u l t i p l e t s p l i t t i n g , and X is a measure o f t h e r a t i o o f t h e f o u r t h t o s i x t h o r d e r CEF p o t e n t i a l s . The CEF s t a t e s a r e t h e n I r6(doublet ) + I r7(double) + 3 rg(quartets). 989
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The.energy level splittlngs (E/W) f o r Er ~ (J - 1 5 / 2 ) i n a c u b i c CEF a s a f u n c t i o n o f X, t h e L e a , L e a s k , a n d Wolf p a r a m e t e r ( f r o m Re£. 5 ) .
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T h e o b s e r v e d 9 GHz EPR d e r l v a c l v e slghal (upper curve) of Yl_cH1.92:Erc for c = 1400 ppm a t T = 1 . 8 K. ~ e l o v e r curve is the computer sfmulatlon.
from an (Isotroplc) r~ d o u b l e t . This is in agreement with a previous Nossbauer determlnatlon of the ground state, z Reference to Fig. I shows thaC the r7 ground state Implles -0.48 < X
< +0.58. We a t c r l b u t e the "satelllte" lines+to t h e g . a n d 8~ p o w d e r p a t t e r n s l g n a l s f r o m Er ) ions in sites of axial symmetry. These lines are similar to those found by Venturini )'' in
12
Vol. 36, No. 12
ELECTRON PARAMAGNETiC RESONANCE
t h e EPR s p e c t r a o f Er 3+ i n S c H : g r . V e n t u r l n l and R i c h a r d s s have s u g g e s t e d t h e r e t o be a s u f f l c l e n t l y l a r g e gain in the f r e e energy to f a v o r t h e o c c u p a t i o n o f one ( o r two) o f t h e n o r mal~y v a c a n t o c t a h e d r a l s i t e s s u r r o u n d i n g t h e Er ~ ion. This leads t o respectlvely C4v and V4h a x i a l symmetries w i t h CN's 9 and 10. The s a t e l l i t e l i n e s then c o r r e s p o n d t o the powder g,, and gx p a t t e r n s . I n SCHc:Er V e n t u r i n l ~ found t h a t i n c r e a s i n g c from c = 1.75 t o c = 1.91 c a u s e d an i n c r e a s e In t h e I n t e n s l t l e s o f t h e (two p a i r s i n ScH :Er) a x i a l l l n e s . This c Increase in the proportion of the axlal sites was n o t , h o w e v e r , accompanled+by any change In t h e ground s t a t e o f t h o s e Er 3 i o n s s t i l l i n cub i c symmetry. Hence, w h i l e i n c r e a s i n g t h e h y d r o g e n c o n c e n t r a t i o n a p p a r e n t l y I n c r e a s e s the number o f a x l e 1 s i t e s o c c u p i e d by Er ~- i o n s , i t d o e s n o t g r e a t l y change t h e X p a r a m e t e r o f t h e remaining cubic sites. In order to determine the r e l a t i v e populat i o n s o f Er ~+ i o n s i n t h e v a r i o u s s l t e symmet r i e s we have made computer s l m u l a t i o n s o f the low t e m p e r a t u r e (T < 4.2 K) e x p e r i m e n t a l s p e c tra. The i n p u t p a r a m e t e r s f o r t h e s e e l m u l a t l o n s ~ a r e t h e g ( r 7 ) , g,,, g1, t h e r e l a t i v e s i t e populations, the (metallic) l l n e s h a p e asymmetry r a t i o , A/H, and t h e s i n g l e i o n l l n e w l d t h . The l a t t e r two p a r a m e t e r s a r e assumed the same f o r i o n s i n c u b i c and a x l a l s y m m e t r l e s . From the 9 GHz d a t a shown i n F i g . 2 we d e t e r m i n e t h a t t h e r e l a t i v e p o p u l a t i o n s o f c u b i c to C4v a x i a l s i t e s a r e i n t h e r a t i o 2 : 1 . At 1.4 GHz, a correct d e t e r m i n a t i o n o f t h e r? r e s o n a n c e l i n e w i d t h can o n l y be made by t a k i n g t h e g ( F ? ) , g,,, g~ and the c u b i c t o a x l a l s i t e r a t i o d e t e r m i n e d from t h e GHz d a t a , and then a d j u s t i n g the s l n g l e ion l l n e w i d t h and A/B r a t i o t o f i t a computer simul a t i o n w i t h t h e o b s e r v e d s p e c t r u m . In t h e r e s t o f t h i s p a p e r we s h a l l be d i s c u s s i n g the F7 resonance llnewldth as a function o f Er m+ concentration, t e m p e r a t u r e , and measuring f r e q u e n c y . I t i s u s u a l t o c o n s i d e r t h e EPR l l n e w l d t h i n a m e t a l a s t h e sum o f a t e m p e r a t u r e d e p e n d e n t p a r t , AH(T), and a t e m p e r a t u r e i n d e p e n d e n t p a r t , AHres(T=O). The t e m p e r a t u r e d e p e n d e n t p a r t can be
writtenl°'ll: g(gj-1) 2 2
AH(T) gJ
~kB[JH(EF)]2 T + ~B CI AI
+ ~i exp(Al/kBT)
- I
(2)
Here g I s t h e ground s t a t e g - v a l ~ e and g j i s the Land~ g f a c t o r ( g j = 6/5 f o r Er ~ ) . J i s the l o c a l moment to c o n d u c t i o n e l e c t r o n exchange c o n s t a n t and N(E F) t h e d e n s i t y o f s t a t e s a t t h e Fermi l e v e l . The C ~ ' s a r e e v a l u a t e d from t h e m a t r i x e l e m e n t s glv~n i n r e f . 11. Here Ai I s t h e s p l l t t l n g between t h e r~ ground s t a t e and the i-th excited state. We s h a l l use ~ f o r t h e ground s t a t e t o f i r s t e x c i t e d s t a t e e n e r g y d i f f e r e n c e . The f i r s t term i s t h e l l n e a r l v t e m p e r a t u r e d e p e n d e n t c o n t r i b u t i o n e x p e c t e d from an I s o l a t e d d o u b l e t i n t h e a b s e n c e of e x c h a n g e e n h a n c e m e n t , and t h e s e c o n d term i s due to a d d i t i o n a l r e l a x a t l o n t h r o u g h e x c i t e d s t a t e s which a r e mixed by an I s o t r o p l c c o n d u c t i o n e l e c t r o n
991
t o l o c a l moment i n t e r a c t i o n . Lower e x c l t e d s t a t e s g i v e t h e most I m p o r t a n t c o n t r l b u t l o n t o t h e s e c o n d term I n Eq. (2) a t low t e m p e r a t u r e . This e x t r a c o n t r i b u t i o n to the l l n e a r t - ~ p e r a t u r e d e p e n d e n c e o f ~I w i l l become i m p o r t a n t a t T = AI3. I n F l g . 3 we p r e s e n t t h e measured r~ 9 GHz EPR l l n e w l d t h s a s a f u n c t i o n o f t e m p e r a t u r e f o r t h e two s a m p l e s . At low t e m p e r a t u r e s , ~lt i s l i n e a r l y p r o p o r t i o n a l t o t e m p e r a t u r e and t h e s l o p e i s i n d e p e n d e n t o f c o n c e n t r a t i o n as shown i n t h e i n s e r t o f F l g . 3. From t h i s we o b t a i n a v a l u e o f (JN) z = 4.4 x I0 - ~ . T h i s a g r e e s w i t h t h e v a l u e , 3.7 × I0 - b , ~ r e v i o u s l y d e t e r m i n e d from H~ssbauer measuroments. The s m a l l p o s i t i v e g s h i f t f o r t h e r~ ground s t a t e c o u l d i n d i c a t e a p o s i t i v e J ; however, the e x p e r i m e n t s / accuracy i s not r e a l l y s u f f i c i e n t to confirm t h i s . Above c i r c a I0 K, t h e measured l l n e w l d t h d e v i a t e s from t h e l l n e a r e x t r a p o l a t i o n o f t h e low t e m p e r a t u r e b e h a v i o r ; t h i s i s due t o t h e second term i n Eq. (2). C o n s i d e r a t i o n o f F t g . ~ l shows t h a t the n e x t e x c i t e d s t a t e f o r an Er 3T i o n w l t h a r7 ground s t a t e i s e i t h e r a r~ I ) , o r a F6, d e p e n d i n g on t h e v a l u e o f X. However, o n l y r s s t a t e s c o n t r i b u t e t o t h e l i n e w t d t h s i n c e the rs s t a t e i s n o t c o n n e c t e d t o t h e r7 ground s t a t e by an l e o t r o p i c o r a n l s o t r o p l c Iz c o n d u c t i o n e l e c t r o n t o l o c a l moment e x c h a n g e . We have computed t h e l l n e w l d t h u s i n g Eq. (2) and f i n d t h e b e s t f i t t o t h e d a t a I s g i v e n by ~(F~ I) - rT) " 35 ± i0 K. I n F l g . 3 we show two computed c u r v e s f o r ~ = 35 K and X 0 and X = - 0 , 4 . These v a l u e s of X g i v e t h e m a x l mum and t h e minimum l i n e w i d t h s a t any g i v e n temp e r a t u r e f o r f i x e d A. As can be seen, the e x p e r i mental accuracy is Insufficient t o a l l o w any d e t e r m i n a t i o n o f X. A f u r t h e r a n a l y s i s f o r t h e v a l u e o f t h e X p a r a m e t e r , which I n v o l v e s a d e c r e a s e i n s i g n a l i n t e n s i t y when t h e r e i s a n e a r b y r6 s t a t e ( i . e . , x = - 0 . 4 5 ) i s i n c o n c l u s i v e due t o the experimental resolutlon. M~ssbauer s t u d i e s ] on ErH z have found a F6 ground s t a t e and A = 125 K. X i s t h u s l e s s t h a n - 0 . 4 8 and t h e o v e r a l l s p l l t t l n g p a r a m e t e r W i s larger. Shenoy e t a l . I s p e c u l a t e t h a t s i n c e YH2:Er has a r7 ground s t a t e , t h e n X f o r b o t h ErH2 and YH2:Er i s c l o s e t o - 0 . 4 8 , t h e c r o s s i n g between t h e ~6 and r7 ground s t a t e s . Our r e s u l t o f A = 35 K I m p l l e s t h a t t h e W p a r a m e t e r i s r a t h e r s m a l l e r i n YH2:Er t h a n i n ErH z. We r e a son a s f o U o w s : I f , f o r example, X = - 0 . 8 5 (ErH2) and X = - 0 . 4 5 (YH~:Er), t h e n we f i n d the r a t i o o f o v e r a l l s p l l t t l n g s W(ErHz):W(YHz:Er) ffi 2:1. I f , however, X f o r b o t h compounds i s a b o u t - 0 . 4 8 , n e a r t h e ground s t a t e c r o s s i n g s , t h e n W(ErH~):W(~:Er) = 4:1. For X(Yll~:Er) • - 0 . 4 8 , t h e r a t i o o f Wts become l a r g e r . The r e s u l t s f o r t h e r e s l d u a l l l n e v i d t h , AH (T " 0), a r e s ~ a r l z e d i n T a b l e I . AH de~ases with both decreasing concentratlon res and w l t h m e a s u r i n g f r e q u e n c y . A f t e r D a h l b e r g | ~ we write: ~ H r e s ( T = O) - ~f ÷ ~
÷ ycf ÷ 6
(3)
The frequency dependtmt c~ntribution, af, is attributed to a strain i ~ i spread in g-vlclues; the concentration dependemt contribution, Be, is due to dipolar hroad~ing; the frequency and concentration d e p e n d e n t c o n t r i b u t i o n , Y c f , i s c a u s e d
992
ELECTRON PARAMAGNETIC RESONANCE
500
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T (K) F i g . 3.
EPR l i n e w i d t h v s . t e m p e r a t u r e f o r Y l _ c H 1 . 9 2 : E r c , c = 1400 ppm, a t 9 CHz f o r the r7 ground s t a t e . The i n s e r t , which has a d i f f e r e n t s c a l e from the main g r a p h , shows t h e l i n e a r t e m p e r a t u r e d e p e n d e n c e f o r b o t h t h e 1400 ppm and 100 ppm s a m p l e s . The d o t t e d l i n e i s an e x t r a p o l a t i o n o f the l i n e a r low temperature behavior (see insert). Both s o l i d c u r v e s a r e c a l c u l a t e d as e x p l a i n e d i n t h e t e x t u s i n g A - 35 K and X = - 0 . 4 ( l o w e r ) and X - 0 ( u p p e r ) .
by c h a r g e d e n s i t y o s c i l l a t i o n s b r o u g h t a b o u t by t h e d i f f e r e n c e i n i o n s i z e and c h a r g e . We have e x t e n d e d D a h l b e r g e s scheme t o i n c l u d e a f r e q u e n c y and c o n c e n t r a t i o n i n d e p e n d e n t t e r m , 6. E x p e r i m e n t a l l y we f i n d a b e s t fiC by a s s u m i n g y = O, and t h e n d e t e r ~ n e a = 1 . 2 ± 0.3 G/CHz, B - 3 ± 1 G/lO00 ppm, and 6 = 12 ± $ G. I t i s n o t p o s s i b l e t o c a l c u l a t e t h e m a g n i t u d e o f a , but our v a l u e i s o f t h e same o r d e r o f m a g n i t u d e found *~ f o r Ag:Er. The c o n c e n t r a t i o n d e p e n d e n t c o n t r i b u t i o n , B, comp a r e s w e l l t o t h e v a l u e , 2.4 G/lO00 ppm, c a l c u l a t e d f o r a powder due t o d i p o l a r b r o a d e n i n g . Is S i n c e Y and Er have s i m i l a r i o n i c s i z e and e l e c t r o n i c c o n f i g u r a t i o n s , no c h a r g e d e n s i t y o s c i l l a t i o n s s h o u l d e x i s t , and ¥ i s e x p e c t e d t o be z e r o . We n o t e h e r e t h a t t h e e x t r a c o n t r i b u t i o n , 6, t o r e s i d u a l l i n e w t d t h i s n o t due t o one o5 t h e 167Er h y p e r f i n s l i n e s o v e r l a p p i n g t h e c e n t r a l F7 r e s o n a n c e l i n e ; we u s e d i s o t o p i c a l l y e n r i c h e d 166Er. TABLE 1 9.38 GHz
1.4 GHz
1400 ppm
27.8 ± 0 . 3 G
18 ± 2 G
100 ppm
23.8 ± 0 . 3 G
17 ± 2 G
The measured r e s i d u a l (T = O) EPR l i n e w i d t h o f Yl_cH1.9Erc f o r d i f f e r e n t measu r i n g f r e q u e n c i e s and c o n c e n t r a t i o n s .
The Er s÷ i o n s i n s i t e s o f c u b i c sywanatry w i t h e i g h t n e a r e s t n e i g h b o r p r o t o n s w i l l have t h e i r f i e l d s f o r r e s o n a n c e s h i f t e d s l i g h t l y by the transferred hyperflne interaction. We f e e l t h a t t h e most l l k e l y o r i g i n o f t h e 6 term i n t h e F~ r e s i d u a l l i n e w l d t h i s t h e r e s u l t i n g u n r e s o l v e d t r a n s f e r r e d h y p e r f l n e s t r u c t u r e (THYS). The H a m i l t o n l a n f o r t h e . l n t e r a c t l o n between t h e i - t h p r o t o n and t h e Er m~ i o n I s :
'i" :i" :i" ~
(4>
where : . i s t h e l - t h p r o t o n n u c l e a r s p i n and : i s t h e e l e ~ t r o n i c s p i n . We have i g n o r e d t h e n u c l e a r Zeeman temzs which a r e s m a l l e r t h a n t h e t r a n s ferred hyperfine terms, although a full analysis of the Hamiltonlan should take these into acc o u n t . * 6 The t r a n s f e r r e d h y p e r f i n e t e n s o r T has a x i a l symmetry and i t s two c o m p o n e n t s , T0, and T~, a r e n o t n e c e s a a r i l y c o m p a r a b l e i n maKnitude. To f i n d t h e u n r e s o l v e d THUS l t n e v i d t h , t h e i n d i v i d u a l p r o t o n H a m i l t o n i a n s must be stmmed
Vol. 36, No. 12
ELECTRON PARAHAGNETIC RESONANCE
over all possible configurations. We e s t i m a t e that for the eight nearest neighbor protons the t s o t r o p i c t r a n s f e r r e d h y p e r f i n e c o n s t a n t , T, i s a b o u t 1/4 o f t h e l i n e w i d t h o f t h e u n r e s o l v e d structure. Our 6 v a l u e o f 12 ± 5 C t h u s g i v e s a rough e s t i m a t e f o r T b e t w e e n 15 and 45 MHz. This i s comparable to T ~ 37 MHz found f o r CaFz:Yb by Ranon and Hyde. | s I n t h a t c a s e t h e EPR l i n e w i d t h due t o THFS was 24 G and t h e t r a n s f e r r e d h y p e r f i n e c o n s t a n t was i n d e p e n d e n t l y d e t e r m i n e d by an ENDOR measurement. Hence our deduced v a l u e o f 6, t h e f r e q u e n c y and c o n c e n t r a t i o n l n d e p e n d -
993
ent contribution to the residual linewldth in Y H l . ~ z : E r , i s of t h e same o r d e r o f m a g n i t u d e as the transferred hyperflne interaction. ACKNOWLEDGMENTS - We would l l k e t o t h a n k Dr. E. P. Chock who a s s i s t e d i n sample p r e p a r a t i o n . One o f us (CHJ) would l l k e t o t h a n k Dr. E. D. Dahlberg and P r o f . R. A. S a t t e n f o r f r u i t f u l discussions. This work was s u p p o r t e d by t h e U. S. Energy R e s e a r c h and Development A d m i n i s t r a t i o n (Argonne) and by NSF G r a n t No. DMR 78-27129
(UCLA).
References
1. 2. 3.
O . K . Shenoy, B. D. Dunlap, D. G. W e s t l a k e , and A. Dwight, P h y s . Rev. 8 1 4 , 41 (1976). J . S t ~ h r and J . D. C a s h t o n , P ~ s . ReV. B 13, 4805 (1975). E . L . V e n t u r i n t , J . A p p , . P ~ s . 50, 2053
9. i0.
5. 6.
7.
E . L . Venturlnl, BUZZ. Am. Phys. Soe. 2__4, 464 (1979). K . R . Lea, M. J. M. Leask, and W. P. Wolf, J. Phys. Chem. SoZ£ds 23, 1381 (1962). G . K . Shenoy, B. D. Dunlap, D. C. Westlake, and V. Dwight, Jotw'f~Z de P ~ q u e 3.._77,C6, 129 (1976). D. Davldov, C. Rettorl, A. Dixon, K. B a b e r s c h k e , E. P. Chock, and R. Orbach,
Phys. Rev. B 8, 3563 (1973). 8.
W. Zingg, J .
Butter,
and M. Hardlman, Proo.
R. Orbach, M. P e t e r ,
and O. $ h a l t l e l ,
Archlves des So.lenoe (Geneva) 2_~7, f a t s 3,
(1979). 4.
18th CoZZ. Ampere (Nottingham, 1974), p . 4 4 7 . V e n C u r l n i and Y. M. R i c h a r d s , SoZ. St, Coer~. 3._..22,1185 (1979). E.L.
II. 12. 13. 14. 15. 16.
141 (1974). C. R e t t o r i , D. Davidov, and H. M. Klm, Phys. Bey. B 8, 5335 (1973). Nai Li Huang L t u , K. J . L i n g , R. Orbach, Phye. Rev. B 144, 4087 (1976). E. D. D a h l b e r g , F ~ s . Rev. B 1_66, 170 (1977). E. D. D a h l b e r g , Ph.D. t h e s i s , U n i v e r s i t y o f C a l i f o r n i a , Los A n g e l e s , 1978 ( u n p u b l i s h e d ) . R. E. B e h r i n g e r , J. Phzjs. Chem. SoZids 2, 209 (1957). U. Ranon snd J . S. Hyde, Phys. Reo. 14__~1, 259 (1965).
S o l i d S t a t e Coaununications, V o i . 3 6 , p p . 9 8 9 - 9 9 3 . Pergamon P r e s s L t d . 1980. P r i n t e d i n G r e a t B r i t a i n .
ELECTRON PARAMAGNETIC
RESONANCE
C. M. J a c k s o n , J . E l l l o t t , Department
of Physics,
IN Yl_cHi.92:Erc
M. Hardlman, R. Orbach
University of California,
Los Angeles,
CA 90024
and G. K. Shenoy Argonne National Laboratory, Argonne, llllnois 604]5 (Received 25 August 1980 by A. A. Maradudin)
We have investigated t h e EPR of Isotoplcally enriched ISSEr 3+ in YI_cHI.92:Er c where c = i00 and 1400 ppm, at both 1.4 and 9 GHz and between 1.5 and 50 K. Resonance lines were observed from Er 3+ ions in both sites of cublc.symmetry and sites of axial symmetry. We determine the 3~ numbers of Er in cubic, and C. axial symmetry to be in the ratio 2:1. The cubic site resonance llne ~v is at g = 6.85 ± 0.07 and is attributed to a r7 doublet. The llnewtdch has a linear thermal broadening of 3,9 ± 0.05 gauss K -l below circa 7 K. From the nonlinear thermal broadening above this temperature we determine the first excited state, in the cubic crystal field scheme, to be a F8 at 35 ± I0 K above the r7 ground state. We have investigated the origins of the (T - O) residual linewldth for the ions in cubic symmetry, and conclude there to be a small but significant contribution due to unresolved transferred hyperflne structure from the surrounding hydrogen n u c l e i .
The m e t a l d l h y d r l d e s YH:, ErH~, and ScHz a l l have t h e f l u o r i t e (CaF2) s t r u c t u r e . This consists of a simple cubic array of protons with m e t a l i o n s o c c u p y i n g e v e r y o t h e r cube c e n t e r . The m e t a l i o n t h u s o c c u p i e s a s i t e o f c u b i c symm e t r y w i t h c o o r d i n a t i o n number (CN)8. M~ssbauer s t u d i e s 1'2 o f Er ~ doped YH2 have i d e n t i f i e d this cubic site. However, e l e c t r o n paramagneclc r e s o n a n c e (EPR) s t u d i e s s on Er sT doped ScH2 i n d i c a t e t h a t , in s~dicion to the expected cubic symmetry, t h e Er 3 i o n o c c u p i e s a t l e a s t one and p o s s i b l y two t y p e s o f s i t e s w i t h a x i a l synunetry. We r e p o r t h e r e . t h e r e s u l t s o f our EPR meas u r e m e n t s on 16SErS~ i n YHI.92:Er. These meas u r e m e n t s were c a r r i e d o u t wlch s e v e r a l o b j e c t i v e s i n v i e w . We wished ( i ) to d e t e r m i n e t h e p r o p o r t i o n o f a x i a l s i t e s , t h e p r e s e n c e o f which had b e e n r e p o r t e d e a r l i e r , ~ ( l i ) t o i n d e p e n d e n t l y confirm the f e a t u r e s of the c r y s t a l e l e c t r i c f i e l d (CEF) a t t h e c u b i c s i t e s a s d e t e r m i n e d l p r e v i o u s l y , and ( i l l ) t o i n v e s t i g a t e t h e o r i g i n s o f t h e (T " 0) r e s i d u a l EPR l l n e w l d t h , i n p a r t l c u l a r the p o s s i b i l i t y of unresolved t r a n s f e r r e d h y p e r f i n e s t r u c t u r e i n t h e Er m+ r e s o n a n c e due t o t h e s u r r o u n d i n g h y d r o g e n n u c l e l . + The c o n v e n t i o n a l llamiltonlan f o r Er 3 , J 1512, i n a c u b i c c r y s t a l f i e l d i s , a f t e r Lea, L e a s k , and Wolf, s
.
-
w
[
x~+
(l-
o:l Ixl> 13g6oj
These e n e r g y l e v e l s a s f u n c t i o n s o f X and W a r e shown i n F i g . 1. The M ~ s s b a u e r ~ t u d i e s | ' 6 o f ¥H2:Er i n d i c a t e t h a t t h o s e Er J" i o n s i n s i t e s w l t h c u b i c symmetry e x h i b i t a s m a l l low t e m p e r a t u r e Korrlnga relaxation rate. P r e v i o u s works on o t h e r s y s t e m s 7 ' s have t a k e n a d v a n t a g e of s m a l l t h e r m a l b r o a d e n i n g t o examine t h e a d d l t l o n a l b r o a d e n i n g o f t h e EPR l i n e w l d t h produced by t h e r m a l p o p u l a t i o n o f c r y s t a l f i e l d s t a t e s above t h e ground state. This i n t u r n a l l o w s a d e t e r m i n a t i o n o f t h e e n e r g y s e p a r a t i o n between t h e ground and first excited states. We have a p p l i e d t h i s a p p r o a c h t o our m e a s u r e m e n t s . Two samples of Yl_cHi.92:Erc , wlth c = I00 and 1400 ppm, were prepared by doping YHI 92 with Isotropically enriched freEr in a manner described elsewhere. I The 16SEr was 95% abundant, the laVEr 3% abundant, and the r e s i d u e made up of other Er isotopes. The low concentration of 167Er was verified by the low intensity of the 16VEt hyperflne lines in the EPR
spectra. The powdered s a m p l e s were found to c y c l e r e p e a t e d l y t o low t e m p e r a t u r e w i t h o u t any change in t h e s p e c t r a . A l l EPR measurements were made u s i n g homodyne s p e c t r o m e t e r s o p e r a t i n g a t 1.4 and 9 GHz and o v e r t h e t e m p e r a t u r e r a n g e 1.2 t o I00 K. The low f r e q u e n c y measurements were s i g n a l a v e r a g e d when n e c e s s a r y . Temperat u r e s were d e t e r m i n e d by v a p o r p r e s s u r e t h e r m o merry below 4.2 K and by t h e r m o c o u p l e s a t h i g h e r temperatures. F i g u r e 2 shows a t y p i c a l low t e m p e r a t u r e EPR s p e c t r u m , which a t b o t h f r e q u e n c i e s d i s p l a y s an i n t e n s e l l n e b e t w e e n a p a i r of weaker " ~ a t e l 1 ire " lines. The intense llne is from Er 3 ions i n c u b i c symmetry; the o b s e r v e d g - v a l u e of 6.85 ± 0.07 i s v e r y c l o s e t o t h e g = 6.8 e x p e c t e d
(~)
w h e t s O~ and O~ a r e t h e S t e p h e n s O p e r a t o r s , W i s t h e o v e r a l l m u l t i p l e t s p l i t t i n g , and X is a measure o f t h e r a t i o o f t h e f o u r t h t o s i x t h o r d e r CEF p o t e n t i a l s . The CEF s t a t e s a r e t h e n I r6(doublet ) + I r7(double) + 3 rg(quartets). 989
990
ZLZCTP.O, P A R A . ~ T Z C
'
'
'
~SO,A~CZ
E/W
'
l
1
'
Vol.
'
'
3 6 , No.
'
3 0 0
"
2I~
~
-
.
I
I
I
I
v
,
~
o L/"
I
I
Fig.
,
I
I
I
I
!
J
I
I
I
I
I
I
I
I
!
!
I
!
I
!
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!
? I
500G Fig.
I
(2) o.e.,
The.energy level splittlngs (E/W) f o r Er ~ (J - 1 5 / 2 ) i n a c u b i c CEF a s a f u n c t i o n o f X, t h e L e a , L e a s k , a n d Wolf p a r a m e t e r ( f r o m Re£. 5 ) .
I.
'w
I
o.4
I
I
I
I
I
'
'
'
;
1400G 2.
T h e o b s e r v e d 9 GHz EPR d e r l v a c l v e slghal (upper curve) of Yl_cH1.92:Erc for c = 1400 ppm a t T = 1 . 8 K. ~ e l o v e r curve is the computer sfmulatlon.
from an (Isotroplc) r~ d o u b l e t . This is in agreement with a previous Nossbauer determlnatlon of the ground state, z Reference to Fig. I shows thaC the r7 ground state Implles -0.48 < X
< +0.58. We a t c r l b u t e the "satelllte" lines+to t h e g . a n d 8~ p o w d e r p a t t e r n s l g n a l s f r o m Er ) ions in sites of axial symmetry. These lines are similar to those found by Venturini )'' in
12
Vol. 36, No. 12
ELECTRON PARAMAGNETiC RESONANCE
t h e EPR s p e c t r a o f Er 3+ i n S c H : g r . V e n t u r l n l and R i c h a r d s s have s u g g e s t e d t h e r e t o be a s u f f l c l e n t l y l a r g e gain in the f r e e energy to f a v o r t h e o c c u p a t i o n o f one ( o r two) o f t h e n o r mal~y v a c a n t o c t a h e d r a l s i t e s s u r r o u n d i n g t h e Er ~ ion. This leads t o respectlvely C4v and V4h a x i a l symmetries w i t h CN's 9 and 10. The s a t e l l i t e l i n e s then c o r r e s p o n d t o the powder g,, and gx p a t t e r n s . I n SCHc:Er V e n t u r i n l ~ found t h a t i n c r e a s i n g c from c = 1.75 t o c = 1.91 c a u s e d an i n c r e a s e In t h e I n t e n s l t l e s o f t h e (two p a i r s i n ScH :Er) a x i a l l l n e s . This c Increase in the proportion of the axlal sites was n o t , h o w e v e r , accompanled+by any change In t h e ground s t a t e o f t h o s e Er 3 i o n s s t i l l i n cub i c symmetry. Hence, w h i l e i n c r e a s i n g t h e h y d r o g e n c o n c e n t r a t i o n a p p a r e n t l y I n c r e a s e s the number o f a x l e 1 s i t e s o c c u p i e d by Er ~- i o n s , i t d o e s n o t g r e a t l y change t h e X p a r a m e t e r o f t h e remaining cubic sites. In order to determine the r e l a t i v e populat i o n s o f Er ~+ i o n s i n t h e v a r i o u s s l t e symmet r i e s we have made computer s l m u l a t i o n s o f the low t e m p e r a t u r e (T < 4.2 K) e x p e r i m e n t a l s p e c tra. The i n p u t p a r a m e t e r s f o r t h e s e e l m u l a t l o n s ~ a r e t h e g ( r 7 ) , g,,, g1, t h e r e l a t i v e s i t e populations, the (metallic) l l n e s h a p e asymmetry r a t i o , A/H, and t h e s i n g l e i o n l l n e w l d t h . The l a t t e r two p a r a m e t e r s a r e assumed the same f o r i o n s i n c u b i c and a x l a l s y m m e t r l e s . From the 9 GHz d a t a shown i n F i g . 2 we d e t e r m i n e t h a t t h e r e l a t i v e p o p u l a t i o n s o f c u b i c to C4v a x i a l s i t e s a r e i n t h e r a t i o 2 : 1 . At 1.4 GHz, a correct d e t e r m i n a t i o n o f t h e r? r e s o n a n c e l i n e w i d t h can o n l y be made by t a k i n g t h e g ( F ? ) , g,,, g~ and the c u b i c t o a x l a l s i t e r a t i o d e t e r m i n e d from t h e GHz d a t a , and then a d j u s t i n g the s l n g l e ion l l n e w i d t h and A/B r a t i o t o f i t a computer simul a t i o n w i t h t h e o b s e r v e d s p e c t r u m . In t h e r e s t o f t h i s p a p e r we s h a l l be d i s c u s s i n g the F7 resonance llnewldth as a function o f Er m+ concentration, t e m p e r a t u r e , and measuring f r e q u e n c y . I t i s u s u a l t o c o n s i d e r t h e EPR l l n e w l d t h i n a m e t a l a s t h e sum o f a t e m p e r a t u r e d e p e n d e n t p a r t , AH(T), and a t e m p e r a t u r e i n d e p e n d e n t p a r t , AHres(T=O). The t e m p e r a t u r e d e p e n d e n t p a r t can be
writtenl°'ll: g(gj-1) 2 2
AH(T) gJ
~kB[JH(EF)]2 T + ~B CI AI
+ ~i exp(Al/kBT)
- I
(2)
Here g I s t h e ground s t a t e g - v a l ~ e and g j i s the Land~ g f a c t o r ( g j = 6/5 f o r Er ~ ) . J i s the l o c a l moment to c o n d u c t i o n e l e c t r o n exchange c o n s t a n t and N(E F) t h e d e n s i t y o f s t a t e s a t t h e Fermi l e v e l . The C ~ ' s a r e e v a l u a t e d from t h e m a t r i x e l e m e n t s glv~n i n r e f . 11. Here Ai I s t h e s p l l t t l n g between t h e r~ ground s t a t e and the i-th excited state. We s h a l l use ~ f o r t h e ground s t a t e t o f i r s t e x c i t e d s t a t e e n e r g y d i f f e r e n c e . The f i r s t term i s t h e l l n e a r l v t e m p e r a t u r e d e p e n d e n t c o n t r i b u t i o n e x p e c t e d from an I s o l a t e d d o u b l e t i n t h e a b s e n c e of e x c h a n g e e n h a n c e m e n t , and t h e s e c o n d term i s due to a d d i t i o n a l r e l a x a t l o n t h r o u g h e x c i t e d s t a t e s which a r e mixed by an I s o t r o p l c c o n d u c t i o n e l e c t r o n
991
t o l o c a l moment i n t e r a c t i o n . Lower e x c l t e d s t a t e s g i v e t h e most I m p o r t a n t c o n t r l b u t l o n t o t h e s e c o n d term I n Eq. (2) a t low t e m p e r a t u r e . This e x t r a c o n t r i b u t i o n to the l l n e a r t - ~ p e r a t u r e d e p e n d e n c e o f ~I w i l l become i m p o r t a n t a t T = AI3. I n F l g . 3 we p r e s e n t t h e measured r~ 9 GHz EPR l l n e w l d t h s a s a f u n c t i o n o f t e m p e r a t u r e f o r t h e two s a m p l e s . At low t e m p e r a t u r e s , ~lt i s l i n e a r l y p r o p o r t i o n a l t o t e m p e r a t u r e and t h e s l o p e i s i n d e p e n d e n t o f c o n c e n t r a t i o n as shown i n t h e i n s e r t o f F l g . 3. From t h i s we o b t a i n a v a l u e o f (JN) z = 4.4 x I0 - ~ . T h i s a g r e e s w i t h t h e v a l u e , 3.7 × I0 - b , ~ r e v i o u s l y d e t e r m i n e d from H~ssbauer measuroments. The s m a l l p o s i t i v e g s h i f t f o r t h e r~ ground s t a t e c o u l d i n d i c a t e a p o s i t i v e J ; however, the e x p e r i m e n t s / accuracy i s not r e a l l y s u f f i c i e n t to confirm t h i s . Above c i r c a I0 K, t h e measured l l n e w l d t h d e v i a t e s from t h e l l n e a r e x t r a p o l a t i o n o f t h e low t e m p e r a t u r e b e h a v i o r ; t h i s i s due t o t h e second term i n Eq. (2). C o n s i d e r a t i o n o f F t g . ~ l shows t h a t the n e x t e x c i t e d s t a t e f o r an Er 3T i o n w l t h a r7 ground s t a t e i s e i t h e r a r~ I ) , o r a F6, d e p e n d i n g on t h e v a l u e o f X. However, o n l y r s s t a t e s c o n t r i b u t e t o t h e l i n e w t d t h s i n c e the rs s t a t e i s n o t c o n n e c t e d t o t h e r7 ground s t a t e by an l e o t r o p i c o r a n l s o t r o p l c Iz c o n d u c t i o n e l e c t r o n t o l o c a l moment e x c h a n g e . We have computed t h e l l n e w l d t h u s i n g Eq. (2) and f i n d t h e b e s t f i t t o t h e d a t a I s g i v e n by ~(F~ I) - rT) " 35 ± i0 K. I n F l g . 3 we show two computed c u r v e s f o r ~ = 35 K and X 0 and X = - 0 , 4 . These v a l u e s of X g i v e t h e m a x l mum and t h e minimum l i n e w i d t h s a t any g i v e n temp e r a t u r e f o r f i x e d A. As can be seen, the e x p e r i mental accuracy is Insufficient t o a l l o w any d e t e r m i n a t i o n o f X. A f u r t h e r a n a l y s i s f o r t h e v a l u e o f t h e X p a r a m e t e r , which I n v o l v e s a d e c r e a s e i n s i g n a l i n t e n s i t y when t h e r e i s a n e a r b y r6 s t a t e ( i . e . , x = - 0 . 4 5 ) i s i n c o n c l u s i v e due t o the experimental resolutlon. M~ssbauer s t u d i e s ] on ErH z have found a F6 ground s t a t e and A = 125 K. X i s t h u s l e s s t h a n - 0 . 4 8 and t h e o v e r a l l s p l l t t l n g p a r a m e t e r W i s larger. Shenoy e t a l . I s p e c u l a t e t h a t s i n c e YH2:Er has a r7 ground s t a t e , t h e n X f o r b o t h ErH2 and YH2:Er i s c l o s e t o - 0 . 4 8 , t h e c r o s s i n g between t h e ~6 and r7 ground s t a t e s . Our r e s u l t o f A = 35 K I m p l l e s t h a t t h e W p a r a m e t e r i s r a t h e r s m a l l e r i n YH2:Er t h a n i n ErH z. We r e a son a s f o U o w s : I f , f o r example, X = - 0 . 8 5 (ErH2) and X = - 0 . 4 5 (YH~:Er), t h e n we f i n d the r a t i o o f o v e r a l l s p l l t t l n g s W(ErHz):W(YHz:Er) ffi 2:1. I f , however, X f o r b o t h compounds i s a b o u t - 0 . 4 8 , n e a r t h e ground s t a t e c r o s s i n g s , t h e n W(ErH~):W(~:Er) = 4:1. For X(Yll~:Er) • - 0 . 4 8 , t h e r a t i o o f Wts become l a r g e r . The r e s u l t s f o r t h e r e s l d u a l l l n e v i d t h , AH (T " 0), a r e s ~ a r l z e d i n T a b l e I . AH de~ases with both decreasing concentratlon res and w l t h m e a s u r i n g f r e q u e n c y . A f t e r D a h l b e r g | ~ we write: ~ H r e s ( T = O) - ~f ÷ ~
÷ ycf ÷ 6
(3)
The frequency dependtmt c~ntribution, af, is attributed to a strain i ~ i spread in g-vlclues; the concentration dependemt contribution, Be, is due to dipolar hroad~ing; the frequency and concentration d e p e n d e n t c o n t r i b u t i o n , Y c f , i s c a u s e d
992
ELECTRON PARAMAGNETIC RESONANCE
500
I
Vol. 36, No. 12
|
I
I
/
400
3o-
* lOOr~m
/
.~
I &/t'/
=3OO "o o
o
~
z
3
4
I/J/lll
-J 200
/
I00
1400 ppm
0 0
I
I
I
tO
I
I
20
I
30
I
I
40
I
50
T (K) F i g . 3.
EPR l i n e w i d t h v s . t e m p e r a t u r e f o r Y l _ c H 1 . 9 2 : E r c , c = 1400 ppm, a t 9 CHz f o r the r7 ground s t a t e . The i n s e r t , which has a d i f f e r e n t s c a l e from the main g r a p h , shows t h e l i n e a r t e m p e r a t u r e d e p e n d e n c e f o r b o t h t h e 1400 ppm and 100 ppm s a m p l e s . The d o t t e d l i n e i s an e x t r a p o l a t i o n o f the l i n e a r low temperature behavior (see insert). Both s o l i d c u r v e s a r e c a l c u l a t e d as e x p l a i n e d i n t h e t e x t u s i n g A - 35 K and X = - 0 . 4 ( l o w e r ) and X - 0 ( u p p e r ) .
by c h a r g e d e n s i t y o s c i l l a t i o n s b r o u g h t a b o u t by t h e d i f f e r e n c e i n i o n s i z e and c h a r g e . We have e x t e n d e d D a h l b e r g e s scheme t o i n c l u d e a f r e q u e n c y and c o n c e n t r a t i o n i n d e p e n d e n t t e r m , 6. E x p e r i m e n t a l l y we f i n d a b e s t fiC by a s s u m i n g y = O, and t h e n d e t e r ~ n e a = 1 . 2 ± 0.3 G/CHz, B - 3 ± 1 G/lO00 ppm, and 6 = 12 ± $ G. I t i s n o t p o s s i b l e t o c a l c u l a t e t h e m a g n i t u d e o f a , but our v a l u e i s o f t h e same o r d e r o f m a g n i t u d e found *~ f o r Ag:Er. The c o n c e n t r a t i o n d e p e n d e n t c o n t r i b u t i o n , B, comp a r e s w e l l t o t h e v a l u e , 2.4 G/lO00 ppm, c a l c u l a t e d f o r a powder due t o d i p o l a r b r o a d e n i n g . Is S i n c e Y and Er have s i m i l a r i o n i c s i z e and e l e c t r o n i c c o n f i g u r a t i o n s , no c h a r g e d e n s i t y o s c i l l a t i o n s s h o u l d e x i s t , and ¥ i s e x p e c t e d t o be z e r o . We n o t e h e r e t h a t t h e e x t r a c o n t r i b u t i o n , 6, t o r e s i d u a l l i n e w t d t h i s n o t due t o one o5 t h e 167Er h y p e r f i n s l i n e s o v e r l a p p i n g t h e c e n t r a l F7 r e s o n a n c e l i n e ; we u s e d i s o t o p i c a l l y e n r i c h e d 166Er. TABLE 1 9.38 GHz
1.4 GHz
1400 ppm
27.8 ± 0 . 3 G
18 ± 2 G
100 ppm
23.8 ± 0 . 3 G
17 ± 2 G
The measured r e s i d u a l (T = O) EPR l i n e w i d t h o f Yl_cH1.9Erc f o r d i f f e r e n t measu r i n g f r e q u e n c i e s and c o n c e n t r a t i o n s .
The Er s÷ i o n s i n s i t e s o f c u b i c sywanatry w i t h e i g h t n e a r e s t n e i g h b o r p r o t o n s w i l l have t h e i r f i e l d s f o r r e s o n a n c e s h i f t e d s l i g h t l y by the transferred hyperflne interaction. We f e e l t h a t t h e most l l k e l y o r i g i n o f t h e 6 term i n t h e F~ r e s i d u a l l i n e w l d t h i s t h e r e s u l t i n g u n r e s o l v e d t r a n s f e r r e d h y p e r f l n e s t r u c t u r e (THYS). The H a m i l t o n l a n f o r t h e . l n t e r a c t l o n between t h e i - t h p r o t o n and t h e Er m~ i o n I s :
'i" :i" :i" ~
(4>
where : . i s t h e l - t h p r o t o n n u c l e a r s p i n and : i s t h e e l e ~ t r o n i c s p i n . We have i g n o r e d t h e n u c l e a r Zeeman temzs which a r e s m a l l e r t h a n t h e t r a n s ferred hyperfine terms, although a full analysis of the Hamiltonlan should take these into acc o u n t . * 6 The t r a n s f e r r e d h y p e r f i n e t e n s o r T has a x i a l symmetry and i t s two c o m p o n e n t s , T0, and T~, a r e n o t n e c e s a a r i l y c o m p a r a b l e i n maKnitude. To f i n d t h e u n r e s o l v e d THUS l t n e v i d t h , t h e i n d i v i d u a l p r o t o n H a m i l t o n i a n s must be stmmed
Vol. 36, No. 12
ELECTRON PARAHAGNETIC RESONANCE
over all possible configurations. We e s t i m a t e that for the eight nearest neighbor protons the t s o t r o p i c t r a n s f e r r e d h y p e r f i n e c o n s t a n t , T, i s a b o u t 1/4 o f t h e l i n e w i d t h o f t h e u n r e s o l v e d structure. Our 6 v a l u e o f 12 ± 5 C t h u s g i v e s a rough e s t i m a t e f o r T b e t w e e n 15 and 45 MHz. This i s comparable to T ~ 37 MHz found f o r CaFz:Yb by Ranon and Hyde. | s I n t h a t c a s e t h e EPR l i n e w i d t h due t o THFS was 24 G and t h e t r a n s f e r r e d h y p e r f i n e c o n s t a n t was i n d e p e n d e n t l y d e t e r m i n e d by an ENDOR measurement. Hence our deduced v a l u e o f 6, t h e f r e q u e n c y and c o n c e n t r a t i o n l n d e p e n d -
993
ent contribution to the residual linewldth in Y H l . ~ z : E r , i s of t h e same o r d e r o f m a g n i t u d e as the transferred hyperflne interaction. ACKNOWLEDGMENTS - We would l l k e t o t h a n k Dr. E. P. Chock who a s s i s t e d i n sample p r e p a r a t i o n . One o f us (CHJ) would l l k e t o t h a n k Dr. E. D. Dahlberg and P r o f . R. A. S a t t e n f o r f r u i t f u l discussions. This work was s u p p o r t e d by t h e U. S. Energy R e s e a r c h and Development A d m i n i s t r a t i o n (Argonne) and by NSF G r a n t No. DMR 78-27129
(UCLA).
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141 (1974). C. R e t t o r i , D. Davidov, and H. M. Klm, Phys. Bey. B 8, 5335 (1973). Nai Li Huang L t u , K. J . L i n g , R. Orbach, Phye. Rev. B 144, 4087 (1976). E. D. D a h l b e r g , F ~ s . Rev. B 1_66, 170 (1977). E. D. D a h l b e r g , Ph.D. t h e s i s , U n i v e r s i t y o f C a l i f o r n i a , Los A n g e l e s , 1978 ( u n p u b l i s h e d ) . R. E. B e h r i n g e r , J. Phzjs. Chem. SoZids 2, 209 (1957). U. Ranon snd J . S. Hyde, Phys. Reo. 14__~1, 259 (1965).